θ-<italic>D</italic> Approximation Technique for Nonlinear Optimal Speed Control Design of Surface-Mounted PMSM Drives

Abstract

This paper proposes nonlinear optimal controller and observer schemes based on a θ- D approximation approach for surface-mounted permanent magnet synchronous motors (PMSMs). By applying the θ- D method in both the controller and observer designs, the unsolvable Hamilton–Jacobi–Bellman equations are switched to an algebraic Riccati equation and state-dependent Lyapunov equations (SDLEs). Then, through selecting the suitable coefficient matrices, the SDLEs become algebraic, so the complex matrix operation technique, i.e., the Kronecker product applied in the previous papers to solve the SDLEs is eliminated. Moreover, the proposed technique not only solves the problem of controlling the large initial states, but also avoids the excessive online computations. By utilizing a more accurate approximation method, the proposed control system achieves superior control performance (e.g., faster transient response, more robustness under the parameter uncertainties and load torque variations) compared to the state-dependent Riccati equation-based control method and conventional PI control method. The proposed observer-based control methodology is tested with an experimental setup of a PMSM servo drive using a Texas Instruments TMS320F28335 DSP. Finally, the experimental results are shown for proving the effectiveness of the proposed control approach.